A numerical model of fully grouted bolts considering the tri-linear shear bond–slip model

A numerical model of fully grouted bolts is proposed in this study by implementing the tri-linear bond–slip relationship of bolts into the numerical framework presented by Hyett et al. (1996). The bond–slip relationship of bolt–rock interface is simplified and represented by the tri-linear model. The proposed numerical model is characterized by (1) its ability in modeling decoupling mechanism of bolt–rock interface, i.e. the degradation of the interfacial shear bond stress along bolts; (2) its easy implementation in a numerical code. The proposed numerical model is verified with the pullout tests, and good agreements with the experimental results can be observed in terms of axial stress distributions in the bolt, shear stress distributions along the bolt and load–displacement relationship. The proposed model also gives a reasonable prediction on the behavior of bolts installed in the field.     

节理剪切过程中锚杆的变形分析

当锚杆与砂浆的粘结未破坏时，以指数曲线来描述锚杆的侧剪应力分布；而对于锚杆与砂浆的粘结遭到破坏的区段，采用抛物线来拟合。给出了粘结破坏和未破坏两种情况下锚杆的轴应力-轴位移关系，提出利用锚杆拉拔实验数据来反演确定计算中所用到的参数。并在缺少实验数据的情况下，给出了一些参数的估计方法。根据岩石是否遭到挤压破坏，分别给出了锚杆的横向剪应力与横向位移的关系式，分析了剪切过程中锚杆加固节理的剪应力-剪位移关系，讨论了对锚固节理剪切变形刚度有重要影响的一些参数。分析表明．高的岩石单轴抗乐强度、较大的锚固面积比有助于提高锚固节理的剪切刚度。分析还表明，倾斜锚杆加固的节理比垂直锚杆的剪切刚度更大，倾斜锚杆以较小的剪切位移调动了更大的剪切阻力；倾斜锚杆加固的节理抗剪强度比垂直锚杆大，提高锚固面积比能显著提高节理抗剪强度。     

锚固段侧阻力分布的一维滑移-软化半数值分析

工程实际表明，预应力锚索（拉力型）锚固段侧阻力的沿程分布多呈单峰上凸曲线，而较多解析推导及半数值分析采用锚固体与孔壁界面的严格全程黏结假设，其计算结果难以解释这一现象。对此，以岩土介质的半无限弹性体假设为基础建立一维力学模型，利用半无限体Mindlin问题的位移解析解，以半数值法求得岩土体与锚固体的孔壁界面位移差值。通过引入侧阻力与位移差值的滑移-软化模型关系，对锚索锚固段的侧阻力分布进行半数值求解探索和算例讨论。相对于锚固段严格全程黏结假设，考虑孔壁界面侧阻力滑移-软化特性更符合实际情况，在张拉力作用下，锚固段始端一定范围的滑移使该区段侧阻力降低，应力向深处转移调整，从而形成侧阻力分布的单峰曲线。     

端部混锚CFRP加固混凝土界面黏结性能模型

现阶段工程实际中CFRP加固钢筋混凝土构件采用的纯粘贴CFRP的方法,容易发生CFRP片材的早期剥离破坏,大大降低了加固效果,采用端部混锚技术可以有效改善该问题.为丰富端部混锚技术加固理论,研究端部混锚技术对CFRP加固混凝土界面黏结性能的影响,结合指数型双参数黏结-滑移本构模型,利用叠加法建立了端部混锚CFRP加固混...     

铝合金筋加固混凝土梁界面黏结性能与剥离承载力研究

通过试验研究与有限元模拟计算,分析了铝合金筋嵌入式加固混凝土梁的破坏模式和承载能力,对比了不同的剥离承载力计算模型,获得了铝合金筋应力和应变以及界面黏结应力沿梁跨度方向的分布曲线,推导出界面黏结-滑移关系和剥离承载力计算公式.结果 表明:铝合金筋加固混凝土梁界面剥离破坏模式分为界面剥离破坏和混凝土保护层剥离破坏,混凝土...     

A new analytical solution to the mechanical behaviour of fully grouted rockbolts subjected to pull-out tests

A new analytical approach able to predict the mechanical behaviour of fully grouted rockbolts subjected to pull-out tests is proposed in this paper. Input parameters of such approach are: bolt radius, bolt’s Young modulus, displacement of the free end of the bolt and the constitutive law of the rockbolt–grout joint interface. The limited circumstances under which it is accurate to determine such constitutive law from pull-out tests are also presented. A solution for the load–displacement curve obtained during pull-out tests has been developed and is detailed in the case of a tri-linear bond-slip model. Comparison with experimental results obtained via in situ pull-out tests has led to the validation of this approach.     

考虑水致弱化及应变梯度的断层岩爆分析

研究了岩石含水量对断层．围岩系统稳定性及岩爆(冲击地压)对韧性断层变形的影响。含水量不仅影响岩石强度，也对应力．应变曲线应变软化阶段斜率有影响。基于梯度塑性理论和水致弱化函数，得到了剪切带内部的塑性剪切应变、总剪切应变及塑性剪切位移的分布规律。此外，还得到了不同含水量时剪力．塑性剪切位移的关系。研究结果表明：随着岩石含水量的增加，塑性剪应变降低，塑性剪切位移降低；含水量越大，则弹性阶段越短，耗散势能越小，外力功越小，断层岩爆释放的弹性能量也越小；岩石的含水量增加，则断层．围岩系统不容易发生失稳。     

端部锚固CFRP板加固RC梁IC剥离过程非线性分析1

端部锚固预应力碳纤维增复合板(Carbon Fiber Reinforcement Polymer Laminate,简称CFRP板)加固钢筋混凝土结构目前最为常见的抗弯加固方式,为探讨端部锚固CFRP加固RC梁IC剥离过程的起始和演化,文章基于部分黏结作用复合梁理论,利用内聚力开裂模型模拟界面层的剥离过程,通过引入含残余强度的四线性黏结滑移本构模型模拟CFRP板与钢筋混凝土梁之间相对滑移带来的界面的变形协调和应力变形行为的非线性特征和软化特性,得到单一裂缝模式下中间裂缝剥离过程中相应的界面黏结剪应力,相对滑移量、CFRP板轴力分布以及加固构件整体荷载 跨中位移,荷载 跨中CFRP板应变的响应曲线,并与文献提供的试验数据进行对比。结果表明,理论计算结果与试验结果基本一致,可以反映端部锚固CFRP板加固混凝土梁的实际受力状态,为端部锚固CFRP板加固混凝土梁的受力分析和设计提供了理论参考。     

土遗址用变径木锚杆锚固机理数值模拟研究

基于室内拉拔试验的物理模型,利用FLAC3D建立变径木锚杆拉拔数值计算模型,分析了变径木锚杆锚固系统的荷载传递规律、界面剪应力分布和传递规律、浆体土体应力场和位移场,并通过数值试验研究锚孔直径、锚杆直径和锚固长度对锚固效果的影响。研究结果表明:数值试验结果与室内拉拔试验结果较为吻合,证明数值模拟木锚杆拉拔过程的可行性和科学性;木锚杆浆体界面剪应力沿锚固段分布不均,主要集中在锚固段顶端和末端的0.1m范围内,末端界面剪应力呈增大的趋势与其变径的结构特征有关,其变径的特点在一定程度上提高了木锚杆的抗拔力;变径木锚杆同时具有拉力型和压力型锚杆的特征,径向具有剪胀作用;锚固影响因素中锚孔直径、锚固长度对木锚杆抗拔力影响显著,而锚杆直径对其影响相对较小;提出了木锚杆极限抗拔力计算公式。     

不同类型预应力锚索锚固性能现场试验对比研究

 在对锚索锚固段剪应力分布模式进行弹塑性理论分析的基础上,开展拉力集中型、拉力分散型、压力分散型锚索的现场破坏性试验,对3类锚索的剪应力分布特征、承载能力、荷载–位移曲线进行对比分析,结果表明：在弹性状态下,3类锚索锚固体上的峰值剪应力均出现在集中力作用点近端0.5 m范围内,且随着荷载增加而增大;进入塑性状态后,上述0.5 m范围最先出现脱黏滑移,峰值剪应力逐渐向锚固体中部转移,脱黏段的残余剪应力约为峰值的1/3;由于拉力分散型锚索的剪应力分布更加均匀、有效锚固段长度更长,其承载能力相比拉力集中型提高31.1%;压力分散型锚索锚固体由于受压产生径向膨胀,其与土体之间的黏结强度增大,因而承载能力比拉力分散型提高17.7%;从荷载–位移曲线来看,压力分散型锚索具有更好的位移延性和抗变形能力,在土体锚固中优势明显。     

Modelling of debonding along the fixed anchor length

Debonding of the fixed length of ground anchorages is presented, concentrating on the failure behaviour of the bond at the proximal end of the fixed length. The dynamic effects of debonding along the fixed length are discussed in particular, with specific reference to dynamic testing. The static effects in terms of load distribution are also reviewed by comparing pull out tests undertaken on laboratory anchorages bonded using resin grout to results from a bond model included in a dynamic model. Bond models, which allow the dynamic effect of the debonding to be observed, are proposed for inclusion in the dynamic model. These models are an elastic–plastic yielding model with some residual load capacity and a model with reduced stiffness once the plastic-yielding regime has been entered. Simulations of an anchorage system including these bond models show both a change in load distribution and a drop in the first natural frequency due to debonding. Simulation of a case study is undertaken using the model and the results show good agreement with the measured field data.     

围岩中原始垂直地应力对圆形隧洞全长注浆 岩石锚杆应力分布模式的影响分析

 通过分析原始垂直地应力对圆形地下洞室塑性区半径、围岩体塑性区和弹性区内岩体的位移变化以及对锚杆应力分布的影响,揭示原始垂直地应力对锚杆锚固效果的影响。研究结果表明,弹性区内任一点的应力大小与垂直地应力有关,而塑性区内任一点的应力与原始垂直地应力无关;随着垂直地应力的增大,巷道塑性区半径也在不断增大,二者之间呈明显的非线性关系;塑性区的径向位移及隧洞壁的最大位移也随之增大。同时,根据围岩与锚杆的相互作用,建立全长注浆岩石锚杆在圆形隧洞围岩中的应力分布解析本构方程。在此解析模型的基础上,对不同垂直地应力作用下锚杆的应力分布模式进行较详细分析,得出随着垂直地应力增大,锚杆的摩阻力和轴向载荷也随之增大,并且锚杆端部的应力集中现象更加明显,当锚杆端部的摩阻力超过围岩的容许抗剪强度时,则锚杆与围岩发生开裂破坏,故在设计与施工中应予以考虑。最后,提出提高和改善由于锚头开裂导致锚固效果降低的方法,对全长注浆岩石锚杆施加垫板,能有效改善锚杆的锚固效果。     

张拉荷载下砂浆锚固岩石锚杆的力学分析

砂浆锚固岩石锚杆在张拉荷载下的轴向应力和剪应力分布非常复杂,为了研究这一问题已经进行了大量的试验,根据这些试验得到的应力分布曲线和相关结论,用比较简单的数学表达式对锚杆交界面上的复杂的剪应力分布情况进行理论描述。在交界面已经破坏的部分,剪应力近似为0,随着锚杆埋深的增加剪应力由0线性增加到其抗剪强度,然后再呈指数形式衰减到0。根据上述数学描述进行实例计算,计算得到的轴向应力和剪应力分布曲线与实测应力分布曲线基本吻合,表明用数学表达对锚杆交界面上的剪应力分布情况进行比较准确的描述是切实可行的。     

岩体离层作用下锚杆受力特性全历程分析

 针对岩体离层作用下锚杆受力特性全历程分析问题,基于锚固界面的双指数曲线模型,采用荷载传递方法,建立离层作用下锚杆受力特性的非线性解答,分析离层发展全历程过程中锚杆轴力和界面剪应力分布,以及岩体离层–锚杆轴力曲线的特性,并采用模型试验数据进行对比验证。结果表明：锚杆轴向应变的计算值与实测结果基本一致。离层发展过程中,锚杆轴力呈现先增大后减小的特性,且在离层发展后期具有明显的非线性特征。离层产生的锚杆轴力和界面剪应力均呈现明显的不均匀分布和非线性特征,且二者均随着离层的发展向两端传递。离层位置对锚杆的受力特性有很大影响：离层位于锚杆中心时,其两侧的锚杆轴力与界面剪应力均成对称分布,且随着离层发展的演变规律相同;离层偏离锚杆中心时,两侧锚杆轴力与界面剪应力分布则明显不同,界面剪应力在离层位置处存在着跳跃点,且锚固长度较小一侧的锚固界面先产生塑性变形直至整体滑移破坏,决定了锚杆所能承受的离层和抗拔荷载大小。研究结果为岩体离层作用下锚杆的受力分析提供了理论参考。     

A review on the performance of conventional and energy-absorbing rockbolts

This is a review paper on the performances of both conventional and energy-absorbing rockbolts manifested in laboratory tests. Characteristic parameters such as ultimate load, displacement and energy absorption are reported, in addition to load-displacement graphs for every type of rockbolt. Conventional rockbolts refer to mechanical rockbolts, fully-grouted rebars and frictional rockbolts. According to the test results, under static pull loading a mechanical rockbolt usually fails at the plate; a fully-grouted rebar bolt fails in the bolt shank at an ultimate load equal to the strength of the steel after a small amount of displacement; and a frictional rockbolt is subjected to large displacement at a low yield load. Under shear loading, all types of bolts fail in the shank. Energy-absorbing rockbolts are developed aiming to combat instability problems in burst-prone and squeezing rock conditions. They absorb deformation energy either through ploughing/slippage at predefined load levels or through stretching of the steel bolt. An energy-absorbing rockbolt can carry a high load and also accommodate significant rock displacement, and thus its energy-absorbing capacity is high. The test results show that the energy absorption of the energy-absorbing bolts is much larger than that of all conventional bolts. The dynamic load capacity is smaller than the static load capacity for the energy-absorbing bolts displacing based on ploughing/slippage while they are approximately the same for the D-Bolt that displaces based on steel stretching.     

Shear‐displacement diagram of steel plate shear walls with precompression from adjacent frame columns

An analytical model of the unstiffened steel plate shear wall (SPSW) considering precompression from the adjacent frame columns is proposed and experimentally verified. First, the distribution and transferring of the gravity loads between boundary columns and the infill steel plate was proposed. Second, the shear‐displacement diagram of the SPSW under compression–shear interaction was obtained, and to further consider the global bending deformation, the shear‐displacement diagram of the SPSW under compression–shear–bending interaction was obtained. Third, the load‐carrying capacities and deformations at the state of elastic buckling of the infill steel plate, the yield of Zones I and III, the yield of Zone II, and the yield of the boundary frame were presented. Finally, cyclic loading test on four scaled one story single bay unstiffened SPSWs under different axial forces at the top of the columns was carried out to verify the proposed analytical model. Shear‐displacement relationship, shear capacity, and envelope curves of the specimens were compared with the predicted values. Results indicate that the proposed analytical model can reasonably predict the decrease of the shear load capacity and stiffness of the SPSWs due to the existence of the axial load at the boundary columns.     

Interfacial stress analysis of RC beams strengthened with hybrid CFS and GFS

The mechanical performances of the interface between the concrete and the fiber reinforced polymer (FRP) are investigated using nonlinear finite element method (FEM) in this paper. The paper focuses on simulating the entire debonding process of the FRP sheets. The interfacial stress levels between the carbon fiber sheet and the glass fiber sheet (CFS–GFS) as well as that between CFS and CFS are compared. A parametrical study was carried out to show how the mechanical performances have been influenced by the load, the elastic modulus, the thickness of adhesive layer and the width of FRP sheets. The simulation results show that the interfacial stresses at the ends of the beam increase with the load and the elastic modulus, but decrease with the thickness of the adhesive layer. The interfacial stresses almost do not vary with the width of FRP. The numerical results of the interfacial stresses have good agreement with analytical results. The numerical results show that it is an effective method for CFS–GFS hybrid fiber sheets to strengthen concrete structures. Hybrid fiber sheets can efficiently reduce interfacial shear stresses of FRP sheets and meanwhile prevent interfacial normal stresses from reaching a high stress level. The results of this numerical study are beneficial to understand the mechanical behaviour of the material interface and design the hybrid FRP reinforced concrete structures.     

Modelling the FRP-concrete delamination by means of an exponential softening law

Among rehabilitation strategies, bonding of Fibre Reinforced Polymers (FRP) plates is becoming more and more popular, especially for what concerns concrete structures. The performance of the interface between FRP and concrete is one of the key factors affecting the behaviour of the strengthened structure. Up to now, closed-form analytical solutions exist only for the local bond-slip law with linear softening. The aim of the present paper is to show that analytical solutions can be achieved also assuming an exponential decaying softening law. Accordingly, the expressions for the interfacial shear stress distribution and the load-displacement response are derived for the different loading stages. A full parametric analysis of the problem has been performed, highlighting the size effect on the structural behaviour as well as the effects of the bond length, of the FRP stiffness and of the interface cohesive law. A comparison with other analytical models as well as with experimental data available in the literature concludes the paper.     

Modeling the pullout behavior of fiber reinforced polymer bars from concrete

This paper presents a numerical investigation of pullout behavior of fiber reinforced polymer (FRP) bar from concrete matrix. As an attempt to capture the debonding process, a progressive damage model is used. Interfacial stress distribution for different load level is analyzed. The effects of embedded length, diameter of FRP bar and bond strength on the load-loaded end displacement are studied. The numerical results indicate that the bond stress decreases gradually from loaded end to embedded end along embedded bar length. The debonding initially starts from loaded end and propagates to embedded end as load increasing. The embedded length and bond strength affect the load-loaded end displacement curves significantly while the diameter of the FRP bar has no obvious effect on these curves. The numerical results have a good agreement with the experimental investigation.     

基于能量原理的压力型锚杆数值模拟计算

根据能量原理,推导了压力型锚杆的轴力与位移计算式。其中锚固体与周围土层的黏结力计算采用弹塑性剪切位移模型,并考虑因位移过大而发生土层卸荷的情况。提出了最小势能原理在压力型锚杆问题中的应用方法,并给出了能量方程的程序求解流程。最后通过算例分析了压力型锚杆在各级荷载下的轴力、位移以及剪应力分布情况,进一步讨论了压力型锚杆的荷载–位移曲线,计算了压力型锚杆极限锚固长度。得出的结论：①压力型锚杆在大部分荷载下都处于弹性工作阶段,一旦进入塑性状态,就表明即将达到承载力极限;②考虑土层卸荷情况的锚固体能量传递理论可以解释压力型锚杆极限锚固长度的存在。